29.15.15 problem 423

Internal problem ID [5021]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 15
Problem number : 423
Date solved : Tuesday, March 04, 2025 at 07:43:42 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

\begin{align*} y y^{\prime }+4 \left (1+x \right ) x +y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 37

ode:=y(x)*diff(y(x),x)+4*(1+x)*x+y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y \left (x \right ) &= \sqrt {{\mathrm e}^{-2 x} c_{1} -4 x^{2}} \\ y \left (x \right ) &= -\sqrt {{\mathrm e}^{-2 x} c_{1} -4 x^{2}} \\ \end{align*}

✓ Mathematica. Time used: 6.146 (sec). Leaf size: 47

ode=y[x] D[y[x],x]+4(1+x)x+y[x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\sqrt {-4 x^2+c_1 e^{-2 x}} \\ y(x)\to \sqrt {-4 x^2+c_1 e^{-2 x}} \\ \end{align*}

✓ Sympy. Time used: 0.593 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(4*x + 4) + y(x)**2 + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \sqrt {C_{1} e^{- 2 x} - 4 x^{2}}, \ y{\left (x \right )} = \sqrt {C_{1} e^{- 2 x} - 4 x^{2}}\right ] \]